Note:
I assume this computer can boot from a USB, but if not, you can burn an iso image, of a Puppy version, to a CD and boot from it.

Install to a USB flash drive and boot from it.
See how you like the Puppy version.
Try a few of them, to find the one you like best and seems to work OK with your hardware.

Download the Puppy version iso file and install to a USB flash drive, using a program you can run from Windows XP to do the install.
There are several.
https://rufus.akeo.ie/https://unetbootin.github.io/_________________I have found, in trying to help people, that the things they do not tell you, are usually the clue to solving the problem.
When I was a kid I wanted to be older.... This is not what I expected

Don't 'wipe' your current OS from the computer until your satisfied with the alternative.

To boot tahrpup from a pentium-M, you may need to add "forcepae" to the boot's kernel arguments, e.g.

kernel /tahr/vmlinuz pmedia=ataflash psubdir=tahr forcepae pfix=fsck

or look for a "nopae" ISO.

When you boot into any Puppy, "First Run" starts. After you've made a couple choices Internet Connection Wizard will open. Tahrpup may not have the driver you need if you need wifi. If it doesn't, ask on the forum about such driver.

The 'rule of thumb' is newer puppies have drivers for newer hardware. That applies to peripherals such as printers and external burners as well.

If your equipment is too old for tahrpup, Lucid is a good choice. So is the 'solid work-horse" Slacko 5.7. For a modern browser, look for watchdog's build of palemoon.

I agree with Mike above. I'm running an older machine than yours, an elderly Dell lappie with less RAM and a P4. It's currently triple-booting with Slacko 570, Lucid 5.2.8.7 and Xenialpup 7.0.8.1 (a slightly earlier, 'beta' version of the current 7.5).

It's not lightning fast, more due to that P4's limitations than anything else.....but it's downright nimble, compared to the XP install that preceded them..!

Any of the above should work okay with that machine. As for the PAE/noPAE thing, well.....the Pentium-M came in two versions, y'see. These are the two 'culprits' in question;-

The 'Banias' was the no-PAE version, the 'Dothan' was the PAE one. Technically speaking, the Banias supported it, but didn't report the fact.....whereas the Dothan both supported it and reported it. And if you want to get really 'technical', the problem was limited to those Pentium M releases with the 400 MHz FSB (front side bus); those running at 533 MHz FSB didn't have this problem (*shrug*). Mind you, it's a moot point anyway, since the whole PAE thing (Physical Address Extensions) was all about whether you could access more than 4 GB of RAM. You have half that; I doubt you're going to have a problem with that anytime soon.....

Personally, I've always run PAE versions, regardless of whether I need to or not.....and with the speed Puppy runs at, you'll be hard-pressed to notice the difference in performance 'twixt them!

Regarding "nopae" and the pentium-M, Mike Walsh has posted the details which, by tomorrow, I'll have forgotten again. The practicalities about it (and drivers) were fresh in my mind as I confronted them yesterday: http://murga-linux.com/puppy/viewtopic.php?p=982963#982963. Before I added the nopae argument the operating system did not reach desktop. It stopped with instructions appearing on the terminal screen telling me that it could not use this operating system.

That I only had 2 Gbs of RAM and wasn't trying to access more than 4 Gbs or RAM wasn't important.

What I take away from this is that computer's are both incredibly fast and incredibly stupid. Some pentium-M computers can't boot operating systems which have kernels that have been configured to access more than 4 Gbs of RAM. But some can but won't because it's manufacturer has provided instructions that it can't. The forcepae argument over-rides that instruction telling it "yes, you can". Obviously, telling it "yes, you can" has no effect if, in fact, it can't. But it's easier for me to remember to try the forcepae argument than remember all the models which can and all the models which can't.

I have Xenial and Artful running very nicely on two laptops of similar specs. An old Toshiba Equium L10, Pentium M "Dothan", 1.5GB ram, and a Samsung V25 with a Pentium 4 with 1GB ram. Both run like they were brand new. I particularly like those two Puppies.

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